1. Field of the Invention
The present invention relates to piezoelectric resonators including a substrate and a vibrator having a structure in which a thin-film portion disposed on the substrate and having at least one piezoelectric thin-film layer is sandwiched between the upper and lower surfaces thereof by at least one pair of upper and lower electrodes disposed on the substrate and opposing each other in the depth direction. More particularly, the present invention relates to a piezoelectric resonator used, for example, as an oscillator for a mobile phone, a wireless LAN, or other apparatus or as an element for a filter or other device, and to a piezoelectric filter, a duplexer, and a communication apparatus, all including the piezoelectric resonator.
2. Description of the Related Art
In a piezoelectric resonator used in a thickness longitudinal oscillation mode, the lengths of opposing sides of an overlapping portion of upper and lower electrodes viewed in the depth direction, that is, when the shape of the overlapping portion of the upper and lower electrodes, which defines a vibrator, is simply a rectangle when viewed in the depth direction, the lengths of the two pairs of opposing sides of the rectangle determine the resonance frequencies of Sn (n=0, 1, 2, 3, etc., where n is a nonnegative integer) oscillation modes. In particular, when the shape of a vibrator is a square when viewed in the depth direction, since the lengths of the two pairs of opposing sides are equal to each other, the resonance frequencies of the Sn (n=0, 1, 2, 3, etc., where n is a nonnegative integer) oscillation modes determined by one pair of opposing sides are the same as those determined by the other pair of opposing sides.
When the shape of the overlapping portion of the upper and lower electrodes is a circle when viewed in the depth direction, since the relationships between the piezoelectric resonator and the oscillatory wavelengths are associated with the diameter of the circle, the resonance frequency of each of the Sn (n=0, 1, 2, 3, etc., where n is a nonnegative integer) oscillation modes is determined for each integer n.
When the piezoelectric resonator has a rectangular overlapping portion, when viewed in the depth direction, which is formed by the upper and lower electrodes, since the length of one pair of opposing sides is different from that of the other pair of opposing sides, the resonance frequencies of the Sn oscillation modes determined by the length of one pair of opposing sides are different from those determined by the length of the other pair of opposing sides, thereby causing spurious oscillations to occur in the vicinities of a large number of resonance frequencies as a whole.
As a result, piezoelectric resonators in which the vibrator is a rectangle when viewed in the depth direction have not been generally used since it is believed that the spurious oscillations caused by the rectangular vibrator have much larger adverse effects than those caused by a square or circular vibrator.
Accordingly, piezoelectric resonators in which the vibrator is simply a square or a circle have been mainly used.
In the piezoelectric resonator in which the shape of the vibrator is a square or a circle as in the conventional manner, when the distance between the opposing sides or the diameter of vibrator is made large so as to obtain a large response of the main oscillation, the frequency width between the resonance point and the anti-resonance point in the frequency characteristics of the piezoelectric resonator widens in general, and accordingly, the piezoelectric resonator is likely to have a reduced Q factor. In other words, when the shape of the overlapping portion of the opposing electrodes is a circle or a square when viewed in the depth direction, as the size thereof becomes larger, the Q factor becomes smaller, thereby leading to an increase in losses of the piezoelectric resonator.
As disclosed, for example, by Japanese Unexamined Patent Application Publication No. 2002-009579, in a known piezoelectric resonator in which the shape of a vibrator is a circle or any shape including a circle therein when viewed in the depth direction and the relationship between the radius r and the thickness of the vibrator satisfies r≧20 t/n (n is a positive integer), the sizes of electrodes of the piezoelectric resonator become large. Also, the reduced Q factor of the piezoelectric resonator causes a problem in which the insertion loss of a filter formed by the piezoelectric resonator increases. FIG. 31 illustrates the phase and impedance characteristics of the known piezoelectric resonator vs. a frequency by way of example.
In this case, since spurious components produce a large number of ripples and also spurious components are produced close to its main oscillation in its frequency range, its resonant characteristics become less stable. For example, the spurious oscillations interfere with the main oscillation.
Also, as disclosed, for example, in Japanese Unexamined Patent Application Publication No. 2000-332568, a known piezoelectric resonator has a vibrator having a trapezoid shape so as to suppress an oscillation mode, appearing in a resonance frequency band of the thickness longitudinal oscillation, among higher harmonics involved in the lateral oscillation modes reflected at the ends of its electrodes.
However, in the piezoelectric resonator having such a vibrator, a diaphragm vibratably supporting the vibrator is required to be larger than a square circumscribing its electrodes. In addition, since the electrodes have irregular shapes, the diaphragm becomes larger than, for example, a square having the same area, thereby making it difficult to reduce the size of the piezoelectric resonator.